The United States and Chile appear headed for a diplomatic showdown over the failure of Chile to prosecute three military officers indicted in Washington in the bombing death of exile Orlando Letelier.

The crisis, should it come, would have serious consequences in Santiago.

U.S. Ambassador George W. Landau who recently returned here after two weeks of consultation in Washington is known to have brought back a clear message from President Carter, Secretary of State Cyrus R. Vance and congressional leaders with whom he met:

Either the evidence gathered by a federal grand jury in Washington is used to prosecute the three Chilean officers or the United States will institute reprisals against Chile.

Although specific measures are a closely held secret the retaliatory action is likely to come in progressively harsher steps, according to close observers of the U.S.-Chilean relationship. The United States might begin by recalling its military mission and later, Landau, these observers said.

Meanwhile, Congress could order military aid still "in the pipeline" halted immediately, the observers add. Next, Congress might require banks in the United States to make public reports on their loans to Chile a step that could make banks less willing to lend to this country, which is heavily dependent on foreign credits.

"The United States is serious about this," one U.S. official here stressed "We are determined to demonstrate that terroism such as the assassination of Letelier will not be tolerated in the streets of Washington."

What the Carter adminstration apparently is offering Chile in return for resolving the Letelier affair to U.S. satisfaction is complete normalization of economic and trade ties and improved political relations.. When he was in New York recently, Landau said that only the Letelier case stands in the way of improved relations.

Chilean Foreign Minister Herman Cubillos is known to be aware of U.S. intentions. Well-informed sources said the United States has made clear to Chilean authorities that, although it originally asked for the extradition of the three -- Gen. Juan Manuel Contreras Sepulveda, Lt. Pedro Espinoza and Capt. Armando Fernandez Larios -- for trial in Washington, a military trial in Chile would be acceptable.

Chile's Supreme Court will meet later this month to hear the U.S. appeal of the court's earlier ruling that barred either extraditing the officers or putting them on trial.

Informed sources indicated that, to satisfy U.S. demands, the court at least would have to order the men to stand trial here and agree that the evidence obtained in theUnited States is sufficient to serve as the basis for prosecution.

This would require the court to overrule its president Israel Borquez who had ruled the evidence was "tainted" because much of it came from Michael Townley, Letelier's admitted assassin, who cooperated with U.S. authorities as part of a plea-bargaining areement for a reduced sentence.

High Chilean officials have in recent days expressed hope that the United States will not react impulssively if the court does not meet the U.S. conditions. Almost no one expects the court to do so. In asking that theUnited States not overreact to an adverse decision by the Supreme Court Chilean officials insist that the case will be turned over to this country's parallel military judicial system after the appeal is decided. The military courts, these officials said, will investigate the officer' alleged involvement in Letelier's murder and the men will be prosecuted if sufficient evidence is found.

These assurances by Chilean officials do not, however, carry much weight at the State Department because of a feeling that Gen. Augusto Pinochet's government has been stalling and playing for time, hoping that the Letelier issue would go away.

Fifteen months ago, the Chileans appointed a general to investigate the Letelier assassination -- time enough according to observers here, for the military courts in Chile to have developed enough evidence to bring their own charges against Contreras, Espinoza and Fernandez Larios if the investigation had been serious.

A high Chilean official said that his country's investigation had been slowed because of an unwillingness by the FBI to give the military investigator here information developed in the United States. This official also warned that retaliation by the Carter administration could lead to a decision by the military junta to tighten its authoritarian grip on the country as well as to increased anti-Amricanism among the government supporters and the military.

"A solution to this matter is possible," the Chilean said, "if only both sides have good faith in one another."

The problem is, after 15 months they don't.